Graphics Programs Reference

In-Depth Information

Use the datainthe table to compute
f
(0

.

9.

2) as accuratelyas possible.

x

0

0

.

1

0

.

2

0

.

3

0

.

4

f
(
x
)

0

.

000 000

0

.

078 348

0

.

138 910

0

.

192 916

0

.

244 981

10.

Using fivesignificant figures in the computations, determine
d
(sin
x
)

/

dx
at
x

=

.

8 from (a) the first forward difference approximation, and (b) the first central

difference approximation. In each case, use
h
that gives the most accurate result

(this requires experimentation).

11.
Use polynomial interpolation to compute
f
and
f
at
x

0

=

0, using the data

x

−

2

.

2

−

0

.

3

0

.

8

1

.

9

f
(
x
)

15

.

180

10

.

962

1

.

920

−

2

.

040

12.

B

R

θ

x

A

C

The crank
AB
of length
R

=

90 mm is rotating at the constant angular speed of

d

θ/

dt

=

5000 rev/min. The position of the piston
C
can be shown to vary with the

angle

θ

as

R
cos

2

sin
2

x

=

θ
+

.

5
2

−

θ

Write aprogram thatcomputes

the acceleration of

the pistonat

θ
=

0
◦
,

5
◦
,

10
◦
,...,

180
◦
by numerical differentiation.

13.

v

γ

C

y

β

α

A

B

a

x

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